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STANDAR 


MEAN  RIGHT-ASCEISIOIS 


OF 


CIRCUMPOLAR  AND  TIME  STARS, 


PREPARED  FOR  THE  USE  OF  THE 


kjU 


U,    S,    COAST    SURVEY. 

1 


A.    D.    BACHE, 

SUPERINTENDENT. 


WASHINGTON: 

GOVERNMENT    PRINTING    OFFICE. 
1862.       / 


UNITED  STATES  COA.ST  SUB  VET. 


(862 


WASHINGTON,  September  13,  1862. 

The  accompanying  determinations  of  star-places  Lave  been  made  by  Dr.  Gould  for  the  use  of  the  telegraph 
longitude  parties  of  the  United  States  Coast  Survey,  especially  in  determining  time  and  instrumental  corrections. 

Their  careful  and  thorough  preparation,  which  is  the  fruit  of  many  years'  labor  in  the  examination  and 
employment  of  all  existing  observations  available  for  the  purpose,  seems  to  entitle  them  to  the  name  of  "Standard 
Right- Ascensions,"  and  these  final  results  are  now  put  in  printed  form,  for  a  more  convenient  distribution  among 
the  parties  of  the  survey  and  astronomers  generally,  than  the  manuscript  form  in  which  they  have  hitherto  been 
circulated. 

A.  D.  BACHE, 

Superintendent ^U,  S.  Coast  Survey. 


623 


UNITED     STATES    COAST     SURVEY. 


CAMBRIDGE,  September  10,  1862. 

SIR  :  A  list  of  Mean  Places  of  48  Circmnpolar  Stars — thirty-six  of  them  being  those  used  by  STRUVE  in  his 
chronometric  expedition  between  Altona  and  Greenwich,  and  four  others  being  the  "  polar  stars, "  generally  so 
called — was  prepared  for  the  use  of  the  Coast  Survey  by  me  and  the  party  under  my  charge  in  1854,  and  first 
printed  in  the  Superintendent's  Annual  Report  for  1855.  A  year  later  it  was  reprinted  with  corrections,  and 
during  the  year  1857  was  improved  as  far  as  possible  with  special  reference  to  its  employment  at  the  Dudley 
Observatory,  in  Albany.  The  method  of  its  formation  was  described  in  some  detail  in  the  sixth  volume  of  the 
Astronomical  Journal. 

At  the  same  time,  and  for  the  same  purpose,  a  similar  redetermination  was  made  of  the  right-ascensions  of 
132  other  fundamental  stars,  favorably  situated  for  use  with  the  circumpolars  in  determining  time  and  azimuth. 
This  has  been  known  as  the  "Time  Star  List,"  and,  although  never  printed  in  its  completed  form,  has  always 
been  at  the  service  of  astronomers  in  this  country. 

The  work  of  collecting  new  observations  and  including  them  in  the  investigation  has  been  continued,  and 
during  the  year  ending  July,  1861,  entirely  new  determinations  were  made  of  the  corrections  needed  for  reducing 
the  right-ascensions  as  given  in  the  principal  catalogues,  and  in  the  several  annual  volumes  of  observations  at 
Greenwich,  Edinburgh,  and  Oxford,  to  the  equinoctial  points  of  the  catalogue  which  I  had  selected  as  the 
fundamental  one,  viz  :  ARGELANDER'  s  DLX  Slellarum  Positiones  Mediae. 

During  the  summer  of  1861  these  new  values  were  employed  for  yet  another  redetermination  of  the  right 
ascensions  and  proper  motions  of  172  stars  out  of  the  180;  and  all  known  observations  and  catalogue  places  since 
the  time  of  BRADLEY,  which  seemed  capable  of  adding  to  the  accuracy  of  the  results,  were  combined  according  to 
the  method  of  least  squares.  No  labor  was  spared  which  promised  a  return,  not  even  the  search  for  and  reduction 
of  crude  observations  scattered  through  the  sundry  volumes  of  unsystematic  and  disconnected  observations  at 
minor  observatories. 

The  small  corrections  for  reducing  to  the  zero  of  ARGELANDER  have  been  determined  :  1st,  by  collation  of  all 
the  right-ascensions  common  to  his  Posit.  Med.  and  to  the  authority  in  question ;  and,  2d,  when  the  number  of 
stars  common  to  both  has  proved  inadequate,  by  a  similar  comparison  with  some  catalogue  for  which  the 
"reduction  to  ARGELANDER"  is  well  determined.  Examination  has  always  been  made  for  terms  which  are  in  any 
way  functions  of  the  declination  or  right-ascension,  as  well  as  for  those  which  are  constant. 

To  the  mean  places,  proper  motions,  and  processional  coefficients,  have  been  added  the  constants  for  reducing 
from  mean  to  apparent  places,  together  with  their  annual  variations.  These  variations  do  not  hold  strictly  for 
1855.0,  but  are  the  average  values  for  the  following  decade,  having  been  obtained  by  computing  the  logarithms 
for  1855  and  1865,  and  dividing  their  difference  by  ten.  They  have  been  computed  also  by  the  differential 
formulas,  for  1855.0;  but  as  these  determinations  excluded  the  proper  motions  and  the  change  in  the  processional 
constants,  they  have  been  used  only  as  a  control,  and  the  former  values  retained  a's  more  convenient. 

Throughout  these  computations  the  Pulkowa  constants  of  precession  and  nutation  have  been  employed. 

The  stars  Sirius,  Castor,  Procyon,  and  611  Cygni,  originally  numbered  35,  39,  40,  115,  are  so  ill-suited  for  the 
determination  of  time,  owing  to  their  magnitude,  variability  of  proper  motion,  or  orbital  revolution,  that  they  are 
now  omitted  from  the  Time-Star  List,  though  without  changing  the  numerical  notation. 

All  the  important  details  and  incidental  results  of  these  investigations  are  prepared  in  proper  form  for  the 
forthcoming  "Records  and  Results  of  the  United  States  Coast  Survey;"  but  since  the  resultant  values  have  been 
for  some  time  adopted  as  standards  of  right-ascension  by  the  Washington  Observatory  and  the  American  Nautical 
Almanac,  as  well  as  in  the  Coast  Survey  parties  and  office,  and  since  constant  applications — as  well  as  various  other 
reasons — render  the  increase  of  copies  desirable,  I  respectfully  suggest  that  the  results  be  put  in  type  in  advance  of 
the  long-deferred  publication  of  the  volume. 

The  table  of  mean  declinations  for  the  circumpolar  stars  is  from  the  Astronomical  Journal  No.  130,  with  a 
slight  change  in  the  arrangement. 

Very  respectfully,  yours,  B.  A.  GOULD. 

Prof.  A.  D.  BACHE,  Superintendent  V.  S.  Coast  Survey. 


UNITED     STATES     COAST     SURVEY. 


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UNITED  STATES  COAST  SURVEY. 


The  arrangement  of  these  tables  scarcely  requires  comment.     The  mean  place  of  a  circumpolar  star  is  given 

by  the  formula  : 

«!  =  a  -f-  (ft.  -f  A)  t  +  B  <2  +  C  t3  +  &c. 

<?i  =  o  +  (X  +  A')  t  +  B'  P  +  C'  e  +  Ac. 

where  t  denotes  the  number  of  years  since  1855.0,  or,  with  a  negative  sign,  the  number  of  years  previous  to  that 

epoch. 

For  the  following  stars,  the  terms  containing  the  fourth  or  higher  powers  of  the  time  become  appreciable 

within  a  century  : 

Polaris. 

51   Cephei. 

/[    firsts  Minoris. 

d  Urs<e  Minoris. 

s 

s 

8 

a 

A     +18.0464 

A     +30.6746 

A     —54.6200 

A     —19.3527 

B     +   0.060321 

B       -  0.007917 

B      -  0.147778 

B       -   0.002762 

C      +   0.00021167 

C       -  0.00004121 

C       -  0.00007653 

C      +   0.00001561 

D     +  0.0000007128 

D     +   0.0000000349 

D     +   0.0000014451 

D     +   0.0000000064 

E     +   0.000000002288 

E     +   0.000000000097 

E     +   0.000000007277 

E        -   0.000000000019 

F     +   0.00000000000697 

F       -  0.00000000000014 

F     +   0.00000000000711 

F        -  0.00000000000001 

G     +   0.0000000000000193 

G       -  0.0000000000001158 

H     +   0.000000000000000040 

II       -  0.000000000000000212 

A'    +19'.217 

1'    -2.7131 

A'    +10.666 

A'  +i"e7i 

B'    _  0.00382 

B'    —0.02208 

B'    --  0.03379 

B'    —0.01404 

C'    --  0.0000139 

C'    +0.0000062 

C'    --  0.0000889 

C'     —0.0000019 

D'    —  0.000000049 

D'   +0.000000023 

D'    --  0.000000092 

D'    +0.000000008 

E'    --  0.00000000018 

E'    —0.00000000002 

E'    +   0.00000000052 

F'    •  -  0.0000  0000  0000  6 

F'    +   0.0000000000025 

G'      -   0.000000000000001 

G'    —  0.000000000000005 

II'    •-  0.00000000000000001 

32  Camelopardalis. 

£  Ursa:  Minoris. 

21  Cassiopca. 

1  Draconis. 

B 

B 

s 

s 

A     +0.3279 

A     -6.4519 

A     +3.8138 

A     +9.2816 

B     +0.001171 

B     +0.001503 

B     +0.000791 

B     —0.004061 

C     —0.00000109 

C     +0.00000060 

C     +0.00000026 

C     +0.00000135 

D     +0.0000000010 

D     —0.0000000004 

D     +0.0000000001 

D     +0.0000000002 

E     —0.000000000001 

9  Draconis. 

4  Draconis. 

12-  Y-.  C.  1879. 

48  Cephei. 

B 

B 

8 

i 

A     +5.3597 

A     +2.9194 

A     —2.4316 

A     +7.2695 

B     —0.001426 

B     —0.000645 

B     —0.001518 

B     +0.001751 

.C      +0.00000046 

C     +0.00000032 

C     -0.00000048 

C     +0.00000021 

D     —0.0000000001 

D     —0.0000000001 

D     —0.0000000001 

D     —0.0000000002 

The  constant  logarithms  for  reduction  from  the  mean  to  the  apparent  equinox  are  given  for  the  epoch  1855.0, 

with  their  annual  variations. 

In  the  Time-Star  List  the  annual  precessions  and  secular  variations  are  given  in  the  ordinary  manner. 

UNITED      STATES     COAST     SURVEY. 


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